CA2292718A1 - High speed analog-to-digital converter and digital-to-analog converter - Google Patents
High speed analog-to-digital converter and digital-to-analog converter Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M1/00—Analogue/digital conversion; Digital/analogue conversion
- H03M1/66—Digital/analogue converters
- H03M1/662—Multiplexed conversion systems
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M1/00—Analogue/digital conversion; Digital/analogue conversion
- H03M1/12—Analogue/digital converters
- H03M1/1205—Multiplexed conversion systems
- H03M1/121—Interleaved, i.e. using multiple converters or converter parts for one channel
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Abstract
An high speed analog-to-digital converter, for converting an analog input signal (u(t)) with a maximum frequency (F max) to a digital output signal (x(n)) with an output sampling rate (F s) at least double the maximum frequency (F max) comprises a plurality of analog narrowband filters (F0-F M-1) for filtering the analog input signal (u(t)) to produce a corresponding plurality of narrowband signals (X0-X M-1). Each narrowband filter has a passband. The sum of the gains of the narrowband filters at any frequency within an operating frequency band of the plurality of narrowband filters is substantially unity. Each of a corresponding plurality of analog-to-digital converter units (AD0-AD M-1) comprises a sample-and-hold device (SH) and a quantizer (Q). The sample-and-hold devices are clocked by a corresponding plurality of clock signals (.PHI.0-.PHI.M-1), respectively, each of the plurality of clock signals having a frequency at least double the bandwidth of the corresponding narrowband filter and an integer division of said predetermined sampling rate. The converter also comprises sampling and summing circuitry for sampling the outputs of the analog-to-digital converter units sequentially at the predetermined sampling rate (Fs) and summing the resulting sampled signals to produce the digital output signal (x(n)). The frequencies of the plurality of clock signals, and their phase-displacements relative to the output sampling clock signal, are such that each sample of the analog-to-digital converter output signal corresponds to a sampling edge of a different one of the sample-and-hold clock signal.
Description
HIGH SPEED ANALOG-TO-DIGITAL CONVERTER
AND DIGITAL-TO-ANALOG CONVERTER
BACKGROUND OF THE INVENTION
TECHNICAL FIELD
The invention relates to analog-to-digital and digital-to-analog converters, and is especially applicable to high speed analog-to-digital converters for wireless communications.
BACKGROUND ART
High speed analog-to-digital converters and digital-to-analog converters are used in wireless telecommunications systems, where digital receivers are preferred, for high speed instruments, for example oscilloscopes, and for various other applications.
Typically, an analog-to-digital converter comprises a clock-driven sample-and-hold circuit, which samples the analog signal at intervals and holds the sample values, and a quantizer which converts each quantized sample into a digital numerical representation.
Typically, the quantizer will compare the sample value with a number of different voltage thresholds in order to determine the value of the sample to within a fairly small band and represent it digitally. It is desirable to provide high resolution as well as high speed, but these tend to be incompatible. Higher resolutions entail more comparisons, i.e. with a larger number of discrete voltage thresholds, which will increase the processing time required to perform the calculations.
One of the fastest A/D converters, known as the "Flash ADC", applies the sample value to a bank of comparators, each of which compares it with a different reference or threshold value. The outputs of the bank of comparators are applied to a Gray code decoder. Unfortunately, such Flash A/D converters require a ladder network of accurate resistors, preferably laser-trimmed, and so are expensive to produce.
Consequently, most high speed devices presently available commercially have limited resolution are able to digitize a 500 MHz analog signal. Current applications, however, may require conversion of signals at 1 GHz and higher.
In order to convert higher . frequency signals, it has been proposed to time-interleave two or more such high speed A/D converters. In a paper entitled "Time Interleaved Converter Arrays", IEEE Journal of Solid-State Circuits, Vol. SC-15, No.
6, December 1980, William C. Black, Jr., et al, disclosed a time interleaved A/D
AND DIGITAL-TO-ANALOG CONVERTER
BACKGROUND OF THE INVENTION
TECHNICAL FIELD
The invention relates to analog-to-digital and digital-to-analog converters, and is especially applicable to high speed analog-to-digital converters for wireless communications.
BACKGROUND ART
High speed analog-to-digital converters and digital-to-analog converters are used in wireless telecommunications systems, where digital receivers are preferred, for high speed instruments, for example oscilloscopes, and for various other applications.
Typically, an analog-to-digital converter comprises a clock-driven sample-and-hold circuit, which samples the analog signal at intervals and holds the sample values, and a quantizer which converts each quantized sample into a digital numerical representation.
Typically, the quantizer will compare the sample value with a number of different voltage thresholds in order to determine the value of the sample to within a fairly small band and represent it digitally. It is desirable to provide high resolution as well as high speed, but these tend to be incompatible. Higher resolutions entail more comparisons, i.e. with a larger number of discrete voltage thresholds, which will increase the processing time required to perform the calculations.
One of the fastest A/D converters, known as the "Flash ADC", applies the sample value to a bank of comparators, each of which compares it with a different reference or threshold value. The outputs of the bank of comparators are applied to a Gray code decoder. Unfortunately, such Flash A/D converters require a ladder network of accurate resistors, preferably laser-trimmed, and so are expensive to produce.
Consequently, most high speed devices presently available commercially have limited resolution are able to digitize a 500 MHz analog signal. Current applications, however, may require conversion of signals at 1 GHz and higher.
In order to convert higher . frequency signals, it has been proposed to time-interleave two or more such high speed A/D converters. In a paper entitled "Time Interleaved Converter Arrays", IEEE Journal of Solid-State Circuits, Vol. SC-15, No.
6, December 1980, William C. Black, Jr., et al, disclosed a time interleaved A/D
converter which used four sample-and-hold circuits and four quantizers and a multiplexer to obtain analog-to-digital conversion of an analog signal having a frequency four times that of the signal handled by each converter. In a paper entitled "A 1-GHz 6-bit ADC
System", IEEE Journal of Solid-State Circuits, Vol. SC-22, No. 6, December 1987, Ken Poulton et al disclosed a time-interleaved analog-to-digital converter capable of a sampling rate of one Gigasample per second using four sample-and-hold circuits and four quantizers. However, instead of a multiplexer, Poulton et al's converter used four memory banks read sequentially. In both cases, the time-interleaved converter arrays used offset clock signals for the four different sample-and-hold circuits.
Black et al's multiplexer and Poulton et al's memory readout, however, operated at the speed of the system clock which was four times the speed of the individual sample-and-hold clock signals. Consequently, the sample-and-hold circuits operated at only one quarter of the overall sampling rate. A disadvantage of such time-interleaved converters is that phase fitter is produced because the offset clock signals are not precisely 90 degrees out of phase with each other, and errors arise because of variations in the high-speed clock which operates the multiplexer or memory readout. Also, the sample-and-hold circuits each see the full wideband signal, which places limitations on their capabilities.
The problem of obtaining both high speed and high resolution has been addressed by a number of people. In a paper entitled "High Speed A/D Conversion Using QMF
Banks", Proceedings of IEEE International Symposium on Circuits and Systems (1990), Petraglia et al disclosed a technique for performing A/D conversion using quadrature mirror filter banks. Petraglia et al used an analysis filter bank which comprised a bank of switched capacitance filters and a bank of downsamplers. The downsampled subband signals were converted by a bank of A/D converter units and then applied to a synthesis filter bank which comprised a bank of upsamplers and a bank of digital filters. Although Petraglia et al's approach avoids the need for offset clock signals, and hence avoids the phase fitter problem, it is not entirely satisfactory because it uses switched capacitance filters. Discrete time-switched capacitance filters limit the speed and introduce switching noise, reducing signal-to-noise ratio. Reducing signal-to-noise ratio reduces resolution.
US Patent No. 5,568,142 issued October 22, 1996 (Velazquez et a~, disclosed an A/D converter using an analog analysis filter bank and a digital synthesis filter bank.
The use of an analog (continuous time) analysis filter bank avoids the problems associated with discrete time switched capacitor filters. However, with present technology, it would be extremely difficult to achieve 1 Gigasample per second conversion rates with the analog-to-digital converter disclosed by Velazquez et al. In particular, Velazquez et al use several 64 tap digital filters in the synthesis filter bank.
Hence, with a rate of 1 Gigasample per second, each digital filter would have to perform 65 x 109 multiplication operations per second and 64 x 10~ addition operations per second. With current technology, this number of operations is not feasible.
SUMMARY OF THE INVENTION
The present invention seeks to eliminate, or at least mitigate, the disadvantages of these known analog-to-digital converters.
According to one aspect of the present invention, there is provided an analog-to-digital converter for converting an analog input signal (u(t)) having a frequency up to a predetermined maximum frequency (Fm"~ to a digital output signal (x(n)) having a predetermined output sampling rate (F~ equal to at least double the maximum frequency (F~, the analog-to-digital converter comprising a plurality of analog narrowband filters (Fo-FM_l; FL,FH,FP) for filtering the analog input signal (u(t)) to produce a corresponding plurality of narrowband signals (Xo-XM_,; XL,XH,XP), each narrowband filter having a passband, the sum of the gains of the narrowband filters at any frequency within the passbands of the plurality of narrowband filters being substantially unity, a corresponding plurality of sample-and-hold devices (SHo-SHM_,; SHL,SH11,SHP) clocked by a plurality of clock signals (~o-~M_I~ ~u~z)~ respectively, each of the plurality of clock signals having a frequency at least double the bandwidth of the corresponding narrowband filter, and a plurality of quantizers (Qo-QM_1) each connected to a respective one of the sample-and-hold devices (SHo-SHM_,) and operable to provide a digitized value of each sample held by the corresponding sample-and-hold device, the converter further comprising sampling and summing means (l2,Ro-RM_,; 121,122,14; 12,141,142; RL,RH,RP) for sampling and summing the outputs of the quantizers to produce said digital output signal (x(n)), the sampling being carried out sequentially at the predetermined sampling rate (Fs) in response to an output clock signal (CLK; ~2), the frequencies and phase-relationships of the plurality of clock signals (øo-~M-1; ~1,~203) being such that each sample point of the output clock signal (CLK; ~2) coincides with a sample point of one of the plurality of clock signals (~o-~M-,; ~1,~2; ~1,~2,~s) In one preferred embodiment of the invention, the plurality of narrowband filters all have the same bandwidth equal to one half of the predetermined output sampling rate (Fs) divided by the number (M) of said narrowband signals, and the plurality of clock signals (~o-~M-,) all have the same frequency equal to the predetermined sampling rate (FS) divided by the number (M) of narrowband signals and are phase-displaced relative to each other by one cycle of such same frequency divided by the number (M) of clock signals.
In an alternative embodiment, the plurality of analog narrowband filters have non-uniform bandwidths for filtering the analog input signal (u(t)) to produce a corresponding plurality of narrowband signals (Xo-XM_,) having different bandwidths.
The sample-and-hold devices perform the downsampling function of the usual analysis filter bank. Consequently, providing the narrowband filters meet certain requirements, the plurality of narrowband filters and the plurality of sample-and-hold devices form an analysis filter bank. An important one of the requirements is that, at each frequency in the operating band, the sum of the squares of the magnitudes of the frequency response is equal to unity.
The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description, taken in conjunction with the accompanying drawings, of preferred embodiments of the invention, which are described by way of example only.
BRIEF DESCRIPTION OF DRAWINGS:
Figure 1 is a block schematic representation of a generic M-band analog-to-digital converter according to one aspect of the invention;
Figure 2 is a block schematic diagram of a two-band uniform resolution analog-to-digital converter embodying the invention;
Figure 3 is a timing diagram for the analog-to-digital converter of Figure 2;
Figure 4 is a detail diagram illustrating a modification to the output portion of the analog-to-digital converter of Figure 2;
Figure 5 is a block schematic representation of a second two-band uniform resolution analog-to-digital converter embodying the invention;
Figure 6 is a timing diagram for the analog-to-digital converter of Figure 5;
Figure 7 is a block schematic representation of a mufti-resolution analog-to-digital converter embodying the invention;
Figure 8 is a timing diagram for the mufti-resolution analog-to-digital converter of Figure 7;
System", IEEE Journal of Solid-State Circuits, Vol. SC-22, No. 6, December 1987, Ken Poulton et al disclosed a time-interleaved analog-to-digital converter capable of a sampling rate of one Gigasample per second using four sample-and-hold circuits and four quantizers. However, instead of a multiplexer, Poulton et al's converter used four memory banks read sequentially. In both cases, the time-interleaved converter arrays used offset clock signals for the four different sample-and-hold circuits.
Black et al's multiplexer and Poulton et al's memory readout, however, operated at the speed of the system clock which was four times the speed of the individual sample-and-hold clock signals. Consequently, the sample-and-hold circuits operated at only one quarter of the overall sampling rate. A disadvantage of such time-interleaved converters is that phase fitter is produced because the offset clock signals are not precisely 90 degrees out of phase with each other, and errors arise because of variations in the high-speed clock which operates the multiplexer or memory readout. Also, the sample-and-hold circuits each see the full wideband signal, which places limitations on their capabilities.
The problem of obtaining both high speed and high resolution has been addressed by a number of people. In a paper entitled "High Speed A/D Conversion Using QMF
Banks", Proceedings of IEEE International Symposium on Circuits and Systems (1990), Petraglia et al disclosed a technique for performing A/D conversion using quadrature mirror filter banks. Petraglia et al used an analysis filter bank which comprised a bank of switched capacitance filters and a bank of downsamplers. The downsampled subband signals were converted by a bank of A/D converter units and then applied to a synthesis filter bank which comprised a bank of upsamplers and a bank of digital filters. Although Petraglia et al's approach avoids the need for offset clock signals, and hence avoids the phase fitter problem, it is not entirely satisfactory because it uses switched capacitance filters. Discrete time-switched capacitance filters limit the speed and introduce switching noise, reducing signal-to-noise ratio. Reducing signal-to-noise ratio reduces resolution.
US Patent No. 5,568,142 issued October 22, 1996 (Velazquez et a~, disclosed an A/D converter using an analog analysis filter bank and a digital synthesis filter bank.
The use of an analog (continuous time) analysis filter bank avoids the problems associated with discrete time switched capacitor filters. However, with present technology, it would be extremely difficult to achieve 1 Gigasample per second conversion rates with the analog-to-digital converter disclosed by Velazquez et al. In particular, Velazquez et al use several 64 tap digital filters in the synthesis filter bank.
Hence, with a rate of 1 Gigasample per second, each digital filter would have to perform 65 x 109 multiplication operations per second and 64 x 10~ addition operations per second. With current technology, this number of operations is not feasible.
SUMMARY OF THE INVENTION
The present invention seeks to eliminate, or at least mitigate, the disadvantages of these known analog-to-digital converters.
According to one aspect of the present invention, there is provided an analog-to-digital converter for converting an analog input signal (u(t)) having a frequency up to a predetermined maximum frequency (Fm"~ to a digital output signal (x(n)) having a predetermined output sampling rate (F~ equal to at least double the maximum frequency (F~, the analog-to-digital converter comprising a plurality of analog narrowband filters (Fo-FM_l; FL,FH,FP) for filtering the analog input signal (u(t)) to produce a corresponding plurality of narrowband signals (Xo-XM_,; XL,XH,XP), each narrowband filter having a passband, the sum of the gains of the narrowband filters at any frequency within the passbands of the plurality of narrowband filters being substantially unity, a corresponding plurality of sample-and-hold devices (SHo-SHM_,; SHL,SH11,SHP) clocked by a plurality of clock signals (~o-~M_I~ ~u~z)~ respectively, each of the plurality of clock signals having a frequency at least double the bandwidth of the corresponding narrowband filter, and a plurality of quantizers (Qo-QM_1) each connected to a respective one of the sample-and-hold devices (SHo-SHM_,) and operable to provide a digitized value of each sample held by the corresponding sample-and-hold device, the converter further comprising sampling and summing means (l2,Ro-RM_,; 121,122,14; 12,141,142; RL,RH,RP) for sampling and summing the outputs of the quantizers to produce said digital output signal (x(n)), the sampling being carried out sequentially at the predetermined sampling rate (Fs) in response to an output clock signal (CLK; ~2), the frequencies and phase-relationships of the plurality of clock signals (øo-~M-1; ~1,~203) being such that each sample point of the output clock signal (CLK; ~2) coincides with a sample point of one of the plurality of clock signals (~o-~M-,; ~1,~2; ~1,~2,~s) In one preferred embodiment of the invention, the plurality of narrowband filters all have the same bandwidth equal to one half of the predetermined output sampling rate (Fs) divided by the number (M) of said narrowband signals, and the plurality of clock signals (~o-~M-,) all have the same frequency equal to the predetermined sampling rate (FS) divided by the number (M) of narrowband signals and are phase-displaced relative to each other by one cycle of such same frequency divided by the number (M) of clock signals.
In an alternative embodiment, the plurality of analog narrowband filters have non-uniform bandwidths for filtering the analog input signal (u(t)) to produce a corresponding plurality of narrowband signals (Xo-XM_,) having different bandwidths.
The sample-and-hold devices perform the downsampling function of the usual analysis filter bank. Consequently, providing the narrowband filters meet certain requirements, the plurality of narrowband filters and the plurality of sample-and-hold devices form an analysis filter bank. An important one of the requirements is that, at each frequency in the operating band, the sum of the squares of the magnitudes of the frequency response is equal to unity.
The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description, taken in conjunction with the accompanying drawings, of preferred embodiments of the invention, which are described by way of example only.
BRIEF DESCRIPTION OF DRAWINGS:
Figure 1 is a block schematic representation of a generic M-band analog-to-digital converter according to one aspect of the invention;
Figure 2 is a block schematic diagram of a two-band uniform resolution analog-to-digital converter embodying the invention;
Figure 3 is a timing diagram for the analog-to-digital converter of Figure 2;
Figure 4 is a detail diagram illustrating a modification to the output portion of the analog-to-digital converter of Figure 2;
Figure 5 is a block schematic representation of a second two-band uniform resolution analog-to-digital converter embodying the invention;
Figure 6 is a timing diagram for the analog-to-digital converter of Figure 5;
Figure 7 is a block schematic representation of a mufti-resolution analog-to-digital converter embodying the invention;
Figure 8 is a timing diagram for the mufti-resolution analog-to-digital converter of Figure 7;
5 Figure 9 illustrates an octave band filter bank suitable for use in the analog-to-digital converter of Figure 8; and Figure 10 is a schematic diagram of an M-band digital-to-analog converter according to a second aspect of the invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to Figure 1, a high speed analog-to-digital converter for providing a digital output signal x(n) from an analog input signal u(t) comprises a bank of M
narrowband analog filters Fo to FM_l, the input terminals of which are connected in common to an input terminal 11 to receive the analog input signal u(t). The maximum frequency of input signal u(t) is F~. There is a certain degree of overlap between the frequency spectra of the analog filters Fo to FM_,, for reasons which will be explained in more detail later. The output terminals of the analog filters Fo to FM_, are each connected to a corresponding one of the inputs of a plurality of sample-and-hold circuits SHo to SHM_l, respectively, which have their output terminals connected to a corresponding plurality of quantizers Qo to QM_l, respectively, which convert each sample to a corresponding digitized value. Each combination of a sample-and-hold circuit and a quantizer itself constitutes an analog-to-digital converter. Consequently, the sample-and-hold circuits and associated quantizers comprise a bank of analog-to-digital converter units ADo to ADM_, which may be of known construction, for example as used in high speed oscilloscopes. The sample-and-hold circuits SHa to SHM_1 are clocked by clock signals ~o to ~M_,, respectively. The digitized values output from the quantizers Qo to QM_1 are buffered by a plurality of registers Ro to RM_l, respectively, each clocked by a master clock signal CLK having a frequency equal to a predetermined sample rate Fs for the digital output signal x(n). A summing device 12 sums the buffered digitized values.
The output from the summer 12 is passed through an output register R~,~ which buffers the digital output signal x(n). The output register Ro"~ is clocked by a clock ~ which is the inverse of the master clock CLK. The clock signals øo to øM_1 are derived from the master clock signal CLK so that each sampling edge of the master clock signal CLK
coincides with a sampling edge of one of the plurality clock signals.
In order to meet Nyquist criteria, the output sample rate Fs is at least double the maximum input frequency F~.
Providing the narrowband filters Fo to FM_, meet requirements of unity gain mentioned above the bank of narrowband filters and the bank of sample-and-hold devices SHo to SHM_1 form an analysis filter bank. Hence, when the narrowband signals Xo to XM_l, from analog filters Fo to FM_I respectively, have been sampled by sample-and-hold circuits SHo to SHM_l, they comprise subband signals.
The subband signals are low pass, band pass and high pass signals, each having its own spectral information, and each having a sample rate determined by the predetermined sample rate (FS) of the output digital signal x(n) and the bandwidth of the corresponding filter relative to maximum input signal frequency F~. For example, if maximum frequency F~ is equal to 1 GHz., Fs is equal to 2 Gigasamples/second, and the filter bank comprises two equal filter which have the same bandwidth of 500 MHz. , each of the sample-and-hold circuits will operate at 1 Gigasamples/second.
Each sample-and-hold circuit would hold the sample value for two periods of the master clock signal CLK.
The mathematical input-output relationship of the M band embodiment of the invention shown in Figure 1, and additional requirements which, preferably, are met by the narrowband filters, will now be described, for the case where the narrowband filter bank is uniform. In the time domain, signals are represented in lower case, e.g. u(t), x(n). In the frequency domain, upper case is used, e.g. U(jfl), X(e~'").
In the frequency domain, the result of filtering an input signal U(jSl), band-limited to t?,~ rad/sec (k=0 ... M-1), through each of the analog narrowband filters Fo to FM_, whose transfer function is Fr(jn) is Xr(jiI) and is given by, (1) Errors for each of the A/D converter units ADo to ADM_1 are modelled as gain error ak and DC offset error bk. Hence, in the time domain, the relationship between the output signal dr(n) of an ideal A/D converter unit AD and the corresponding narrowband signal xk(n) is given by:
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to Figure 1, a high speed analog-to-digital converter for providing a digital output signal x(n) from an analog input signal u(t) comprises a bank of M
narrowband analog filters Fo to FM_l, the input terminals of which are connected in common to an input terminal 11 to receive the analog input signal u(t). The maximum frequency of input signal u(t) is F~. There is a certain degree of overlap between the frequency spectra of the analog filters Fo to FM_,, for reasons which will be explained in more detail later. The output terminals of the analog filters Fo to FM_, are each connected to a corresponding one of the inputs of a plurality of sample-and-hold circuits SHo to SHM_l, respectively, which have their output terminals connected to a corresponding plurality of quantizers Qo to QM_l, respectively, which convert each sample to a corresponding digitized value. Each combination of a sample-and-hold circuit and a quantizer itself constitutes an analog-to-digital converter. Consequently, the sample-and-hold circuits and associated quantizers comprise a bank of analog-to-digital converter units ADo to ADM_, which may be of known construction, for example as used in high speed oscilloscopes. The sample-and-hold circuits SHa to SHM_1 are clocked by clock signals ~o to ~M_,, respectively. The digitized values output from the quantizers Qo to QM_1 are buffered by a plurality of registers Ro to RM_l, respectively, each clocked by a master clock signal CLK having a frequency equal to a predetermined sample rate Fs for the digital output signal x(n). A summing device 12 sums the buffered digitized values.
The output from the summer 12 is passed through an output register R~,~ which buffers the digital output signal x(n). The output register Ro"~ is clocked by a clock ~ which is the inverse of the master clock CLK. The clock signals øo to øM_1 are derived from the master clock signal CLK so that each sampling edge of the master clock signal CLK
coincides with a sampling edge of one of the plurality clock signals.
In order to meet Nyquist criteria, the output sample rate Fs is at least double the maximum input frequency F~.
Providing the narrowband filters Fo to FM_, meet requirements of unity gain mentioned above the bank of narrowband filters and the bank of sample-and-hold devices SHo to SHM_1 form an analysis filter bank. Hence, when the narrowband signals Xo to XM_l, from analog filters Fo to FM_I respectively, have been sampled by sample-and-hold circuits SHo to SHM_l, they comprise subband signals.
The subband signals are low pass, band pass and high pass signals, each having its own spectral information, and each having a sample rate determined by the predetermined sample rate (FS) of the output digital signal x(n) and the bandwidth of the corresponding filter relative to maximum input signal frequency F~. For example, if maximum frequency F~ is equal to 1 GHz., Fs is equal to 2 Gigasamples/second, and the filter bank comprises two equal filter which have the same bandwidth of 500 MHz. , each of the sample-and-hold circuits will operate at 1 Gigasamples/second.
Each sample-and-hold circuit would hold the sample value for two periods of the master clock signal CLK.
The mathematical input-output relationship of the M band embodiment of the invention shown in Figure 1, and additional requirements which, preferably, are met by the narrowband filters, will now be described, for the case where the narrowband filter bank is uniform. In the time domain, signals are represented in lower case, e.g. u(t), x(n). In the frequency domain, upper case is used, e.g. U(jfl), X(e~'").
In the frequency domain, the result of filtering an input signal U(jSl), band-limited to t?,~ rad/sec (k=0 ... M-1), through each of the analog narrowband filters Fo to FM_, whose transfer function is Fr(jn) is Xr(jiI) and is given by, (1) Errors for each of the A/D converter units ADo to ADM_1 are modelled as gain error ak and DC offset error bk. Hence, in the time domain, the relationship between the output signal dr(n) of an ideal A/D converter unit AD and the corresponding narrowband signal xk(n) is given by:
dk(n) _ (1 +ak~k(n) + bk In the frequency domain, aliasing error will be seen along with the gain error and D.C.
offset error. Hence, in the frequency domain, the output signal Dk(e ~ from each of the A/D converter units ADo to ADM_1 is given by the expression:-Dk(e;~,) = 1 T k ~ Xk j_w - j2xl + bk ~ 2~8(w-2xn t=o T T t=o where b is a delta function, T is the sampling period given by T = ~~ ~ and the term k Xk ~J ~ l ~ is the aliasing error.
Substituting for Xr(jQ) from equation (1) gives:-Dk(ej~) = 1 +ak ~ U Jw _ j2~r1 Fk jw _ j2~1 + bk ~ 2x8(w-2~rlJ
T ~=o T T T T i=o The wideband digital output signal X(e~'") obtained by summing the signals Dk(e~~) from the A/D converter units ADo to ADM_1 is given by:-X(e''") _ ~ Dk (e''") k=0 Combining equations (4) and (5) gives:-M i 1 +ak M i jw _ J~xl jw _ j2~1 Fx + ~ bk ~ 2x8(w-2a~ (6) k=o T r=o T T T T k=o r=o The summation terms in equation (6) can be rearranged and written as, g M-1 M-1 l+a M-1 M-1 U jw - j2al . ~ k F jm - j2~rl + ~ b ~ 2a8(w-2~r~ (~
1=o T T k=o T k T T k=o k l=o Equation (7) can be simplified by substituting functions Ap(e~'~) and Vii, to give:-X(e,w) _ ~ v JT - ~ T
p=0 where Ap(e'°") is the aliasing function for the whole high speed A/D
converter and is given by the expression:-Ap(ei") _ ~ 1 +ak pk ._1~ - J~~P ~ P = 0 . . M-1 k=o T T T
and the total DC offset error ~i for the whole high-speed A/D converter is given by the expression:-a = 2~ ~ bk ~ b (cuM-Zap) (10) k=0 p=0 The condition for avoiding aliasing is:-Ao(e'~) = e'~,~a P - 0 (11) AP(e~") = 0 p = 1 .. (M - 1) (12) where d is the overall system delay, i.e. for the whole high-speed A/D
converter. The condition for zero D.C. offset error is :-is ,a = o In order for the digital output signal x(n) to be a so-called perfect or pseudo-perfect representation of the input signal u(n), the analysis filter bank formed by the analog filters Fo to FM_1 and sample-and-hold circuits SHo to SHM_1 should be designed so that, at any frequency within the operating range, zero to F~"~, the gains of the filters sum to unity, i.e. ~ Fo(jn) ~ Z + ~ Fl(jil) ~ 2+ ......, + ~ Fm.,(jtI) ~ Z = 1 This is analogous to the output of an analysis filter bank being capable of perfect or pseudo-perfect reconstruction using a corresponding synthesis filter bank.
The frequencies and relative phase-displacements of the clock signals ~o to ~M_, are selected so that every sample point of the output signal corresponds to a sample point of one of the clock signals ~o to ~M_,. Where the analog filters Fo-FM_, have the same bandwidth, the clock signals have the same frequency and are phase-shifted uniformly relative to each other by 2x/M radians so as to subdivide each clock period of the input signal u(t) into M equal segments. Hence, for a two-band A-to-D converter, there would be two sample-and-hold circuits clocked by two clock signals 180° out of phase with each other, the data being stored on the rising edges of each of the clock signals.
For a four-band converter, the clock signals would be phased at 9f° increments relative to each other.
The implementation and operation of a two-band high speed analog-to-digital converter will now be described with reference to Figures 2 and 3.
Referring to Figure 2, the high speed analog-to-digital converter comprises a high-pass filter FH and a low-pass filter FL with their inputs connected in common to an input terminal 11 to receive the input signal u(t) to be digitized. The narrowband signal XH from the high-pass filter FH is applied to the respective inputs of a pair of sample-and-hold circuits Slip and SH, which are clocked by clock signals ø, and ~2, respectively, which are in antiphase relative to each other so that the sample-and-hold circuits Slia and SHl operate in time-interleaved manner. The samples from the sample-. and-hold circuits SHo and SHl are applied to quantizers Qo and Q,, respectively. In a similar manner, the narrowband signal XL from lowpass filter FL is applied to the inputs of a second pair of sample-and-hold circuits SHZ and SH3 which also are clocked by clock signals ø, and ø2, respectively. The samples from sample-and-hold circuits SH2 and SH3 are applied to quantizers QZ and Q3, respectively.
The quantized values L, and Hl from quantizers Qo and Q,, respectively, are summed by a first summing device 12, and the quantized values Lz and HZ from quandzers Ql and Q2, respectively, are summed by summing device 122. A
switching device 14, conveniently a time multiplexer, clocked by clock signal ~2 , which here serves also as the output clock signal, selects the outputs of summers 12, and 122, alternately, for output as digitized output signal x(n). The switching device 14 is clocked so that, when clock signal ø2 is high, the output of summer 122 is selected.
Conversely, when the clock signal ~2 is low, clock signal ~~ is high and the output is taken from summer 121. Hence, the digitized values in summers 12, and 122 are sampled on both the rising and falling edges of clock signal ~Z, which is equivalent to sampling on the rising edges of main clock signal CLK.
Operation of the two-band analog-to-digital converter of Figure 2 will now be described with reference to the timing diagram in Figure 3. For reference purposes, 5 successive periods of the main clock signal CLK are numbered as T, to T8.
Clock signals ~, and ~2 are derived from a master clock signal CLK, specifically by dividing it by two.
At the beginning of period TI of clock signal CLK a leading edge of clock signal ~1 causes the sample-and-hold circuits SHo and SHl to sample signals XL and XH. The 10 resulting samples, respectively, immediately are quantized to produce values Lll and H"
which are summed by summing device 12, to produce value A". As can be seen from Figure 3, there will be some delay due to the time taken for quantization and also for summing.
At the beginning of interval T2 of main clock CLK, clock signal ø2 causes sample-and-hold circuits SH, and SH3 to sample signals XL and XH. The resulting samples are quantized to produce quantized values h1 and H2, which are summed by summer 122 to produce value A21.
The process is repeated to produce two series of values of A1 and AZ at the poles of switching device 14, vis. Alo, All, A12, A13 and so on at one pole and A2o, A21, AZZ, Ate, and so on at the other pole.
The switching device 14 selects the values alternately at the frequency of main clock signal CLK. Thus, when clock signal ~Z is low, and clock signal ~1 is high, values of A1 are selected. When clock signal ~Z is low and clock signal ~1 is low, values of AZ are selected.
Typically, for example, for an input u(t) having a maximum frequency of 1 gigahertz, the filters FL and FH would be 0-500 MHz and 500-1000 MHz, respectively.
Each of the sample-and-hold circuits SHo-SH3 will sample at a rate of 1 gigasample per second. The output signal rate will be at least 2 gigasamples per second.
Each A/D converter unit samples at one half of the output rate Fa, but each narrowband subband signal is sampled by two sample-and-hold converter units, offset by 180°, so that the effective sampling is at the full output rate.
The analog-to-digital converter of Figure 2 is capable of high accuracy and high speeds without the usual problems associated with time-interleaving. In particular, because the sampled signals X1, and X11 are narrowband signals, the dynamic response requirements for the sample-and-hold circuits SHa-SH3 is reduced.
As illustrated in Figure 4, it would be possible to modify the output portion of the analog-to-digital converter of Figure 2 so as to avoid the use of two summers 121 and 122. Thus, in Figure 4 the outputs Ll and LZ from quantizers Qo and Ql are supplied to a switching device 141, for example a multiplexer, while the output Hl and H2 from the quantizers Q2 and Q3 are supplied to a second switching device 142, for example another multiplexer. The switching devices 141 and 142 are clocked by clock signal ~2, as before. The outputs of the switching devices 141 and 142 are summed by summing device 12 to provide the digitized output signal x(n). With this arrangement, only one summer 12 is needed, but it must be capable of operation at double the rate of summers 121 and 122 of Figure 2.
Although the analog-to-digital converters of Figures 2 and 4 produce very accurate results, acceptable accuracy for many applications can be obtained with fewer sample-and-hold circuits, as illustrated in Figure 5. Thus, in the analog-to-digital converter shown in Figure 5, high pass filter Fll and low pass filter FL have their inputs connected in common to the input terminal to receive the analog signal u(t).
The narrowband signals X11 and Xl, from high pass filter Fll and low-pass filter Fl,, respectively, are applied to sample-and-hold circuits SHII and SHL, respectively. The sample-and-hold circuits SHH and SHL are clocked by clock signals ~1 and ~2, respectively. As in the embodiments of Figures 2 and 4, the clock signals ~1 and ~Z are at one half the sampling rate Fs of the output signal and in anti-phase relative to each other. Hence, the sample-and-hold circuits SHL to SHII perform downsampling, so the high-pass filter Fll, the low-pass filter Fl,, and the two sample-and-hold circuits SHH and SHI, effectively form an analysis filter bank having the "perfect reconstruction/representation" or "pseudo-perfect reproduction/representation"
capabilities previously discussed. The samples from sample-and-hold circuits SHII and SHI, are digitized by quantizers Qll and QL, respectively, to provide digitized values DH
and DL, respectively. The series of values DH and DL from the quantizers Ql, and QH
are buffered by registers RL and Rll clocked by main clock signal CLK. The buffered digital signals AH and AL are summed by summing device 12, the output of which is buffered by an output register Rte, clocked by clock signal ~ , i.e. the inverse of master clock signal CLK, before being output as the digital representation x(n) of the analog input signal u(t).
Operation of the two-band high speed analog-to-digital converter of Figure 5 will now be described with reference to Figure 6 which depicts the timing diagrams for the device.
For reference purposes, successive cycles of the main clock CLK which are shown in Figure 6 are numbered T~ through Tg, inclusive. At the beginning of first period Tl, the rising edge of clock signal ~, causes the sample-and-hold circuit SHL to sample the low-pass narrowband signal XL to produce, and hold, a first sample L,.
Quantizer QL in analog-to-digital converter unit ADL quandzes the sample Ll to produce a corresponding digital representation DLI. The sampling and quantizing take a certain amount of time, which is much less than one period of clock signal ~,. On the following rising edge of main clock CLK, i.e. at the beginning of period TZ, the digital value DL, is clocked into the register RL which stores it as value AL, during periods T2 and T3 of main clock signal CLK, since the value DL, persists at the output of analog-to-digital converter unit ADL when the register RL is clocked again at the beginning of period T3.
The high pass narrowband signal XH is digitized in a similar manner. During the first period T~ of main clock signal CLK, clock signal ~Z is low. On the rising edge of clock signal ~2 at the end of first clock period T~, clock signal ~2 causes the sample-and-hold circuit SHH in analog-to-digital converter unit ADH to sample the narrowband signal XH to acquire and hold sample H,. Quantizer QH quantizes the sample value H, to produce a corresponding digital value DHl and, on the next rising edge of clock signal CLK (start of period T3), transfers the value DH, into register RH which stores it as value AHl for two periods of clock signal CLK.
The summing device 12 sums the instant values of AH and AL continuously and supplies the sum to register R~ which outputs the value on each falling edge of clock CLK (i.e. rising edge of inverse clock ~ ).
Hence, on the falling edge of main clock CLK occurnng in period T3, register R~,~ outputs the value AL, + AH, as the digital representation of the current sample of input signal u(t). While this processing of samples H, and L, is taking place, the process of sampling and quantizing is already being repeated for the next pair of samples. Thus, on the rising edge of clock signal ~1 at the start of period T3, analog-to-digital converter unit ADL acquires a second sample LZ and quantizes it to produce a corresponding digital representation Due, which is stored in register R~.
Likewise, the rising edge of clock signal ~2 at the start of period T4 causes the sample-and-hold circuit SHH in analog-to-digital converter unit ADH to obtain and hold sample H2 which is quantized and stored in register RH. On the next falling edge of main clock signal CLK, the register Ra" outputs the sum ALZ + Am. The sequence is repeated for subsequent samples.
It can be seen from Figure 6 that the values in the registers RH and RL are each stored for two cycles of the main clock signal CLK. However, the contents of the registers RH and RL do not change at the same time, but rather at times which are separated by one clock period of main clock signal CLK. Consequently, the stored values overlap. Because register R~ is clocked at the rate of main clock signal CLK, it samples the sum of the two overlapped signals AH and AL once each clock period.
Providing the analysis filter bank 10 meets the conditions set out hereinbefore, the digital signal x(n) outputted from register R~,~ will be a "perfect or pseudo-perfect representation" of the analog input signal u(t).
If the input signal is a wideband signal having a bandwidth, say, of 500 MHz, the main clock signal CLK must have a minimum frequency of IGHz to meet Nyquist criteria.
It will be seen from Figures 5 and 6, that the analog-to-digital converter units ADH and ADL sample the narrowband signals at a rate which is one half of the output sample rate Fs. For example, for an input signal having a bandwidth of 500 MHz, and an output signal x(n) having a sampling rate Fs of 1 Gigasample/sec, each of the analog-to-digital converter units ADH and ADL samples at a rate of only 500 Megasamples/sec.
Each output sample value is alternately a value which was obtained within the previous half cycle of the main clock CLK and a value which was obtained approximately one cycle previously. At any given time, therefore, the output from a particular one of the A-D converter units ADH and ADL will be current or delayed.
Because the signals supplied to the quantizers QH and QL are, in effect, subband signals, and the analysis filter bank characteristics are carefully selected to ensure correlation between these subband signals, in particular in accordance with the principles of "perfect or pseudo-perfect reconstruction", the output signal x(n) is an accurate representation of the analog input signal u(t).
It should be noted that the high speed analog-to-digital converter uses what, in effect, is an analysis filter bank to divide the input signal into subband signals, but does not use the usual synthesis filter bank to recombine them. It should also be noted that an analysis filter bank comprises a set of narrowband filters followed by a set of downsamplers. In this case, the sample-and-hold units SHL and SHH provide the downsampling because each samples at one half of the rate of the output signal, and at least double the bandwidth of the corresponding one of narrowband filters F~
and FH.
The analog-to-digital converter units ADH and ADL do not operate directly upon the input signal but rather upon the narrowband signals. Consequently, the need for wideband analog-to-digital converter units is avoided. Because the analog-to-digital converter units operate with a narrow bandwidth, they are less susceptible to phase errors. For an input signal u(t) having a maximum frequency of, say, 500 MHz, and two narrowband filters FL and FH of equal bandwidth, each analog-to-digital converter unit would handle only 250 MHz bandwidth. Consequently, since each analog-to-digital converter unit is still clocked at 500 samples per second, it oversamples the narrowband signal and so is less affected by phase error. It should also be noted that, because the outputs from the two A-D converter units ADS and ADH are added, differences between the two A-to-D converter units would offset each other, making the device less susceptible to gain error.
An advantage of the embodiment of Figure 5 is that it requires only two A-D
converter units ADL and ADH to produce a satisfactory output suitable for use in most wireless telecommunications applications, and the like. If even greater accuracy is desired, however, such as for instrumentation applications, and the expense of additional analog-to-digital converter units can be tolerated, the analog-to-digital converters of Figures 2 and 4 might be preferred. The embodiments of Figures 2 and 4 potentially are more accurate than that of Figure 5 because they do not rely upon correlation between the instant and previous values of the two narrowband signals XH and XL.
Rather, each narrowband signal is sampled at the full output rate.
There are applications where a mufti-resolution A/D converter would be desirable. Such a mufti-resolution AlD converter is illustrated in Figure 7.
The analog input signal u(t) having a frequency up to a maximum F~ is supplied in common to the inputs of a bank of narrowband filters comprising a low pass filter FL, a bandpass filter FP and a high pass filter FH, all having different bandwidths. For example, the bandwidths might be 0-250 MHz, 250-500 MHz and 500 MHz to 1 GHz, respectively.
The narrowband signals XL, XP and XH from the filters FL, FP and FH are supplied to three sample-and-hold circuits SHL, SHP and SHH, respectively. The samples from the sample-and-hold circuits SHL, SHP and SHH are quantized by quantizers QL, QP
and QH, 5 respectively, to provide digitized samples DL, DP and DH which are clocked into registers RL, RP and RH, respectively. The outputs of the registers are connected to respective inputs of a summing device 12 which sums the outputs GL, GP and GH from the registers RL, RP and RH and supplies the sum to output register Rte, which acts as a buffer.
Registers RL, RP and RH are clocked by main clock signal CLK at the predetermined 10 sampling rate F, while output register Ra"~ is clocked by the inverse clock signal '~ , i.e. on the falling edges of main clock signal CLK.
The frequencies of clock signals ~1, ~2 and ~3, and their relative phases, are selected so that each sampling point/edge of the main clock signal CLK
substantially coincides with one of the sampling points/edges of the clock signals ~,, ~2, and ~3. For 15 example, if Fm"~ is 1 GHz, the bandwidths of filters FL, FP and FH are 0-250 MHz, 250-500 MHz and 500 MHz-1 GHz, respectively, and the output sample rate Fs is equal to at least 2 Gigasamples/second, suitable frequencies for clock signals øl, ~Z, and ~3 are 500 MHz, 500 MHz and 1 GHz, respectively.
Again, the filters FL, FP and FH, together with the sample-and-hold circuits SHL, SHP and SHH, constitute an analysis filter bank. Also, each combination of a sample-and-hold circuit and a quantizer constitutes an analog-to-digital converter unit.
The filters XL, Xp and XH could comprise an octave filter bank as shown in Figure 9. 1'he octave filter bank comprises a first stage formed by a lowpass filter FLP
and a high pass filter FH having their inputs connected in common to receive the input signal u(t). The narrowband signal from filter FH is the high pass signal XH.
The filtered signal from filter F~ is filtered by additional two filters FL and FP
to provide the low pass signal XL and the bandpass signal XP. Filters FLP and FH would have the same bandwidth, e.g. 500 MHz, and filters FL and FP would have the same, lower bandwidth, e.g. 250 MHz.
The frequency of clock signal ~3 is one half of the rate of master clock signal CLK, and the clock signals ~2 and ~, have the same frequency equal to one half the rate of clock signal ~3.
The operation of the mufti-resolution A/D converter, which is analogous to that of the uniform analog-to-digital converter of Figure 2, will now be described with reference also to Figure 8. At the beginning of clock period T1 of main clock signal CLK, the rising edge of clock signal ~, causes sample-and-hold circuit SHL to sample narrowband signal XL. The sample is quantized by quantizer QL to produce quantized sample DL, which is clocked into register RL, as value GLI, by the rising edge at the beginning of main clock period T2. The sample-and-hold circuit SHL holds the sample for one complete cycle of clock signal ~1, and the digitized value Gel remains in the register RL for a similar length of time, specifically until the end of period TS of main clock signal CLK.
At the beginning of period T2 of clock signal CLK, the rising edge of clock signal ~3 causes sample-and-hold circuit SHH to sample high pass signal XH and the sample is quantized by quantizer QH to produce digitized value DH,. The corresponding digitized value GH, is clocked into register RH at the beginning of main clock period T3 of main clock signal CLK. In this case, digitized value GH, is stored in register RH for only two periods of main clock signal CLK.
At the beginning of period T3 of main clock signal CLK, the rising edge of clock signal ~2 causes sample-and-hold circuit SHP to sample bandpass signal XP.
1'he resulting sample is quantized by quantizer Qp and clocked into register RP by the rising edge at the beginning of period T4 of main clock signal CLK. The corresponding digitized value GPl is stored in register RP for four periods of main clock signal CLK.
The summing device 12 (Figure 9) sums the outputs of registers RL, RP and RH
at the beginning of each period of main clock signal CLK. Allowing for processing time, the result, GLl and G~ and GHO is available by the next falling edge of clock signal CLK, and is clocked into output register R~,~. Values G~ and GHO are, of course, values previously obtained by a similar process.
The sequence is repeated for subsequent samples of the narrowband signals XL, XP and XH to produce a series of values, GL, + G~ + GHO, GL, + G~ + GH,, GLl +
GPl + GHI, and so on as the digital output signal x(n) at the sampling Fe.
As before, in view of the continuous nature of the analog signal u(t) and the analysis filter bank characteristics of the A-D converter, x(n) is an accurate representation of input signal u(t), even though each of the individual sample-and-hold circuits SHL, SHP and SHH does not necessarily sample at double the maximum frequency of the corresponding one of the narrowband signals XL, XP and XH.
Various modifications may be made to the above-described embodiments without departing from the scope of the present invention. Thus, in Figures 3, 6 and 8, sampling is carried out on the rising edges of the clock signals, but it would also be possible to carry out sampling on the falling or trailing edges, in which case suitable alternative components would be selected.
It should be noted that embodiments of the invention differ from time-interleaved D-A converters in that the inputs to the A/D converter units are subband signals of the wide-band continuous time input signal u(t). Another important difference in embodiments of this invention is that, unlike the time interleaved converters, the outputs are not time-multiplexed, but rather are summed.
Referring now to Figure 10, a digital-to-analog converter suitable for converting a high speed digital signal x(n) to an analog signal u(t) comprises a bank of lower speed D-A converter units DA.o, DA, ... DAM_, having their inputs connected in common to receive the input digital signal x(n). The outputs of the D-A converters DAo-DAM_1 are applied to the inputs of a bank of narrowband filters Po, P, - PM-~, respectively, the outputs of which are summed by analog summing device 20 to form the analog output signal u(t). The bank of narrowband filters Po - PM-, and summing device 20 constitute an analog synthesis filter bank.
The bank of D-A converters DAa - DAM_1 are clocked by a corresponding plurality of clock signals ~o - ~M-, which all have the same frequency but are offset in phase relative to each other, conveniently uniformly. As in the case of the A-D
converter described hereinbefore, the phase offsets are such that each sampling point of the input signal x(n) coincides with a sampling point of one of the clock signals ~1 - ~M-1.
Although embodiments of the invention have been described and illustrated in detail, it is to be clearly understood that the same are by way of illustration and example only and not to be taken by way of the limitation, the spirit and scope of the present invention being limited only by the appended claims.
offset error. Hence, in the frequency domain, the output signal Dk(e ~ from each of the A/D converter units ADo to ADM_1 is given by the expression:-Dk(e;~,) = 1 T k ~ Xk j_w - j2xl + bk ~ 2~8(w-2xn t=o T T t=o where b is a delta function, T is the sampling period given by T = ~~ ~ and the term k Xk ~J ~ l ~ is the aliasing error.
Substituting for Xr(jQ) from equation (1) gives:-Dk(ej~) = 1 +ak ~ U Jw _ j2~r1 Fk jw _ j2~1 + bk ~ 2x8(w-2~rlJ
T ~=o T T T T i=o The wideband digital output signal X(e~'") obtained by summing the signals Dk(e~~) from the A/D converter units ADo to ADM_1 is given by:-X(e''") _ ~ Dk (e''") k=0 Combining equations (4) and (5) gives:-M i 1 +ak M i jw _ J~xl jw _ j2~1 Fx + ~ bk ~ 2x8(w-2a~ (6) k=o T r=o T T T T k=o r=o The summation terms in equation (6) can be rearranged and written as, g M-1 M-1 l+a M-1 M-1 U jw - j2al . ~ k F jm - j2~rl + ~ b ~ 2a8(w-2~r~ (~
1=o T T k=o T k T T k=o k l=o Equation (7) can be simplified by substituting functions Ap(e~'~) and Vii, to give:-X(e,w) _ ~ v JT - ~ T
p=0 where Ap(e'°") is the aliasing function for the whole high speed A/D
converter and is given by the expression:-Ap(ei") _ ~ 1 +ak pk ._1~ - J~~P ~ P = 0 . . M-1 k=o T T T
and the total DC offset error ~i for the whole high-speed A/D converter is given by the expression:-a = 2~ ~ bk ~ b (cuM-Zap) (10) k=0 p=0 The condition for avoiding aliasing is:-Ao(e'~) = e'~,~a P - 0 (11) AP(e~") = 0 p = 1 .. (M - 1) (12) where d is the overall system delay, i.e. for the whole high-speed A/D
converter. The condition for zero D.C. offset error is :-is ,a = o In order for the digital output signal x(n) to be a so-called perfect or pseudo-perfect representation of the input signal u(n), the analysis filter bank formed by the analog filters Fo to FM_1 and sample-and-hold circuits SHo to SHM_1 should be designed so that, at any frequency within the operating range, zero to F~"~, the gains of the filters sum to unity, i.e. ~ Fo(jn) ~ Z + ~ Fl(jil) ~ 2+ ......, + ~ Fm.,(jtI) ~ Z = 1 This is analogous to the output of an analysis filter bank being capable of perfect or pseudo-perfect reconstruction using a corresponding synthesis filter bank.
The frequencies and relative phase-displacements of the clock signals ~o to ~M_, are selected so that every sample point of the output signal corresponds to a sample point of one of the clock signals ~o to ~M_,. Where the analog filters Fo-FM_, have the same bandwidth, the clock signals have the same frequency and are phase-shifted uniformly relative to each other by 2x/M radians so as to subdivide each clock period of the input signal u(t) into M equal segments. Hence, for a two-band A-to-D converter, there would be two sample-and-hold circuits clocked by two clock signals 180° out of phase with each other, the data being stored on the rising edges of each of the clock signals.
For a four-band converter, the clock signals would be phased at 9f° increments relative to each other.
The implementation and operation of a two-band high speed analog-to-digital converter will now be described with reference to Figures 2 and 3.
Referring to Figure 2, the high speed analog-to-digital converter comprises a high-pass filter FH and a low-pass filter FL with their inputs connected in common to an input terminal 11 to receive the input signal u(t) to be digitized. The narrowband signal XH from the high-pass filter FH is applied to the respective inputs of a pair of sample-and-hold circuits Slip and SH, which are clocked by clock signals ø, and ~2, respectively, which are in antiphase relative to each other so that the sample-and-hold circuits Slia and SHl operate in time-interleaved manner. The samples from the sample-. and-hold circuits SHo and SHl are applied to quantizers Qo and Q,, respectively. In a similar manner, the narrowband signal XL from lowpass filter FL is applied to the inputs of a second pair of sample-and-hold circuits SHZ and SH3 which also are clocked by clock signals ø, and ø2, respectively. The samples from sample-and-hold circuits SH2 and SH3 are applied to quantizers QZ and Q3, respectively.
The quantized values L, and Hl from quantizers Qo and Q,, respectively, are summed by a first summing device 12, and the quantized values Lz and HZ from quandzers Ql and Q2, respectively, are summed by summing device 122. A
switching device 14, conveniently a time multiplexer, clocked by clock signal ~2 , which here serves also as the output clock signal, selects the outputs of summers 12, and 122, alternately, for output as digitized output signal x(n). The switching device 14 is clocked so that, when clock signal ø2 is high, the output of summer 122 is selected.
Conversely, when the clock signal ~2 is low, clock signal ~~ is high and the output is taken from summer 121. Hence, the digitized values in summers 12, and 122 are sampled on both the rising and falling edges of clock signal ~Z, which is equivalent to sampling on the rising edges of main clock signal CLK.
Operation of the two-band analog-to-digital converter of Figure 2 will now be described with reference to the timing diagram in Figure 3. For reference purposes, 5 successive periods of the main clock signal CLK are numbered as T, to T8.
Clock signals ~, and ~2 are derived from a master clock signal CLK, specifically by dividing it by two.
At the beginning of period TI of clock signal CLK a leading edge of clock signal ~1 causes the sample-and-hold circuits SHo and SHl to sample signals XL and XH. The 10 resulting samples, respectively, immediately are quantized to produce values Lll and H"
which are summed by summing device 12, to produce value A". As can be seen from Figure 3, there will be some delay due to the time taken for quantization and also for summing.
At the beginning of interval T2 of main clock CLK, clock signal ø2 causes sample-and-hold circuits SH, and SH3 to sample signals XL and XH. The resulting samples are quantized to produce quantized values h1 and H2, which are summed by summer 122 to produce value A21.
The process is repeated to produce two series of values of A1 and AZ at the poles of switching device 14, vis. Alo, All, A12, A13 and so on at one pole and A2o, A21, AZZ, Ate, and so on at the other pole.
The switching device 14 selects the values alternately at the frequency of main clock signal CLK. Thus, when clock signal ~Z is low, and clock signal ~1 is high, values of A1 are selected. When clock signal ~Z is low and clock signal ~1 is low, values of AZ are selected.
Typically, for example, for an input u(t) having a maximum frequency of 1 gigahertz, the filters FL and FH would be 0-500 MHz and 500-1000 MHz, respectively.
Each of the sample-and-hold circuits SHo-SH3 will sample at a rate of 1 gigasample per second. The output signal rate will be at least 2 gigasamples per second.
Each A/D converter unit samples at one half of the output rate Fa, but each narrowband subband signal is sampled by two sample-and-hold converter units, offset by 180°, so that the effective sampling is at the full output rate.
The analog-to-digital converter of Figure 2 is capable of high accuracy and high speeds without the usual problems associated with time-interleaving. In particular, because the sampled signals X1, and X11 are narrowband signals, the dynamic response requirements for the sample-and-hold circuits SHa-SH3 is reduced.
As illustrated in Figure 4, it would be possible to modify the output portion of the analog-to-digital converter of Figure 2 so as to avoid the use of two summers 121 and 122. Thus, in Figure 4 the outputs Ll and LZ from quantizers Qo and Ql are supplied to a switching device 141, for example a multiplexer, while the output Hl and H2 from the quantizers Q2 and Q3 are supplied to a second switching device 142, for example another multiplexer. The switching devices 141 and 142 are clocked by clock signal ~2, as before. The outputs of the switching devices 141 and 142 are summed by summing device 12 to provide the digitized output signal x(n). With this arrangement, only one summer 12 is needed, but it must be capable of operation at double the rate of summers 121 and 122 of Figure 2.
Although the analog-to-digital converters of Figures 2 and 4 produce very accurate results, acceptable accuracy for many applications can be obtained with fewer sample-and-hold circuits, as illustrated in Figure 5. Thus, in the analog-to-digital converter shown in Figure 5, high pass filter Fll and low pass filter FL have their inputs connected in common to the input terminal to receive the analog signal u(t).
The narrowband signals X11 and Xl, from high pass filter Fll and low-pass filter Fl,, respectively, are applied to sample-and-hold circuits SHII and SHL, respectively. The sample-and-hold circuits SHH and SHL are clocked by clock signals ~1 and ~2, respectively. As in the embodiments of Figures 2 and 4, the clock signals ~1 and ~Z are at one half the sampling rate Fs of the output signal and in anti-phase relative to each other. Hence, the sample-and-hold circuits SHL to SHII perform downsampling, so the high-pass filter Fll, the low-pass filter Fl,, and the two sample-and-hold circuits SHH and SHI, effectively form an analysis filter bank having the "perfect reconstruction/representation" or "pseudo-perfect reproduction/representation"
capabilities previously discussed. The samples from sample-and-hold circuits SHII and SHI, are digitized by quantizers Qll and QL, respectively, to provide digitized values DH
and DL, respectively. The series of values DH and DL from the quantizers Ql, and QH
are buffered by registers RL and Rll clocked by main clock signal CLK. The buffered digital signals AH and AL are summed by summing device 12, the output of which is buffered by an output register Rte, clocked by clock signal ~ , i.e. the inverse of master clock signal CLK, before being output as the digital representation x(n) of the analog input signal u(t).
Operation of the two-band high speed analog-to-digital converter of Figure 5 will now be described with reference to Figure 6 which depicts the timing diagrams for the device.
For reference purposes, successive cycles of the main clock CLK which are shown in Figure 6 are numbered T~ through Tg, inclusive. At the beginning of first period Tl, the rising edge of clock signal ~, causes the sample-and-hold circuit SHL to sample the low-pass narrowband signal XL to produce, and hold, a first sample L,.
Quantizer QL in analog-to-digital converter unit ADL quandzes the sample Ll to produce a corresponding digital representation DLI. The sampling and quantizing take a certain amount of time, which is much less than one period of clock signal ~,. On the following rising edge of main clock CLK, i.e. at the beginning of period TZ, the digital value DL, is clocked into the register RL which stores it as value AL, during periods T2 and T3 of main clock signal CLK, since the value DL, persists at the output of analog-to-digital converter unit ADL when the register RL is clocked again at the beginning of period T3.
The high pass narrowband signal XH is digitized in a similar manner. During the first period T~ of main clock signal CLK, clock signal ~Z is low. On the rising edge of clock signal ~2 at the end of first clock period T~, clock signal ~2 causes the sample-and-hold circuit SHH in analog-to-digital converter unit ADH to sample the narrowband signal XH to acquire and hold sample H,. Quantizer QH quantizes the sample value H, to produce a corresponding digital value DHl and, on the next rising edge of clock signal CLK (start of period T3), transfers the value DH, into register RH which stores it as value AHl for two periods of clock signal CLK.
The summing device 12 sums the instant values of AH and AL continuously and supplies the sum to register R~ which outputs the value on each falling edge of clock CLK (i.e. rising edge of inverse clock ~ ).
Hence, on the falling edge of main clock CLK occurnng in period T3, register R~,~ outputs the value AL, + AH, as the digital representation of the current sample of input signal u(t). While this processing of samples H, and L, is taking place, the process of sampling and quantizing is already being repeated for the next pair of samples. Thus, on the rising edge of clock signal ~1 at the start of period T3, analog-to-digital converter unit ADL acquires a second sample LZ and quantizes it to produce a corresponding digital representation Due, which is stored in register R~.
Likewise, the rising edge of clock signal ~2 at the start of period T4 causes the sample-and-hold circuit SHH in analog-to-digital converter unit ADH to obtain and hold sample H2 which is quantized and stored in register RH. On the next falling edge of main clock signal CLK, the register Ra" outputs the sum ALZ + Am. The sequence is repeated for subsequent samples.
It can be seen from Figure 6 that the values in the registers RH and RL are each stored for two cycles of the main clock signal CLK. However, the contents of the registers RH and RL do not change at the same time, but rather at times which are separated by one clock period of main clock signal CLK. Consequently, the stored values overlap. Because register R~ is clocked at the rate of main clock signal CLK, it samples the sum of the two overlapped signals AH and AL once each clock period.
Providing the analysis filter bank 10 meets the conditions set out hereinbefore, the digital signal x(n) outputted from register R~,~ will be a "perfect or pseudo-perfect representation" of the analog input signal u(t).
If the input signal is a wideband signal having a bandwidth, say, of 500 MHz, the main clock signal CLK must have a minimum frequency of IGHz to meet Nyquist criteria.
It will be seen from Figures 5 and 6, that the analog-to-digital converter units ADH and ADL sample the narrowband signals at a rate which is one half of the output sample rate Fs. For example, for an input signal having a bandwidth of 500 MHz, and an output signal x(n) having a sampling rate Fs of 1 Gigasample/sec, each of the analog-to-digital converter units ADH and ADL samples at a rate of only 500 Megasamples/sec.
Each output sample value is alternately a value which was obtained within the previous half cycle of the main clock CLK and a value which was obtained approximately one cycle previously. At any given time, therefore, the output from a particular one of the A-D converter units ADH and ADL will be current or delayed.
Because the signals supplied to the quantizers QH and QL are, in effect, subband signals, and the analysis filter bank characteristics are carefully selected to ensure correlation between these subband signals, in particular in accordance with the principles of "perfect or pseudo-perfect reconstruction", the output signal x(n) is an accurate representation of the analog input signal u(t).
It should be noted that the high speed analog-to-digital converter uses what, in effect, is an analysis filter bank to divide the input signal into subband signals, but does not use the usual synthesis filter bank to recombine them. It should also be noted that an analysis filter bank comprises a set of narrowband filters followed by a set of downsamplers. In this case, the sample-and-hold units SHL and SHH provide the downsampling because each samples at one half of the rate of the output signal, and at least double the bandwidth of the corresponding one of narrowband filters F~
and FH.
The analog-to-digital converter units ADH and ADL do not operate directly upon the input signal but rather upon the narrowband signals. Consequently, the need for wideband analog-to-digital converter units is avoided. Because the analog-to-digital converter units operate with a narrow bandwidth, they are less susceptible to phase errors. For an input signal u(t) having a maximum frequency of, say, 500 MHz, and two narrowband filters FL and FH of equal bandwidth, each analog-to-digital converter unit would handle only 250 MHz bandwidth. Consequently, since each analog-to-digital converter unit is still clocked at 500 samples per second, it oversamples the narrowband signal and so is less affected by phase error. It should also be noted that, because the outputs from the two A-D converter units ADS and ADH are added, differences between the two A-to-D converter units would offset each other, making the device less susceptible to gain error.
An advantage of the embodiment of Figure 5 is that it requires only two A-D
converter units ADL and ADH to produce a satisfactory output suitable for use in most wireless telecommunications applications, and the like. If even greater accuracy is desired, however, such as for instrumentation applications, and the expense of additional analog-to-digital converter units can be tolerated, the analog-to-digital converters of Figures 2 and 4 might be preferred. The embodiments of Figures 2 and 4 potentially are more accurate than that of Figure 5 because they do not rely upon correlation between the instant and previous values of the two narrowband signals XH and XL.
Rather, each narrowband signal is sampled at the full output rate.
There are applications where a mufti-resolution A/D converter would be desirable. Such a mufti-resolution AlD converter is illustrated in Figure 7.
The analog input signal u(t) having a frequency up to a maximum F~ is supplied in common to the inputs of a bank of narrowband filters comprising a low pass filter FL, a bandpass filter FP and a high pass filter FH, all having different bandwidths. For example, the bandwidths might be 0-250 MHz, 250-500 MHz and 500 MHz to 1 GHz, respectively.
The narrowband signals XL, XP and XH from the filters FL, FP and FH are supplied to three sample-and-hold circuits SHL, SHP and SHH, respectively. The samples from the sample-and-hold circuits SHL, SHP and SHH are quantized by quantizers QL, QP
and QH, 5 respectively, to provide digitized samples DL, DP and DH which are clocked into registers RL, RP and RH, respectively. The outputs of the registers are connected to respective inputs of a summing device 12 which sums the outputs GL, GP and GH from the registers RL, RP and RH and supplies the sum to output register Rte, which acts as a buffer.
Registers RL, RP and RH are clocked by main clock signal CLK at the predetermined 10 sampling rate F, while output register Ra"~ is clocked by the inverse clock signal '~ , i.e. on the falling edges of main clock signal CLK.
The frequencies of clock signals ~1, ~2 and ~3, and their relative phases, are selected so that each sampling point/edge of the main clock signal CLK
substantially coincides with one of the sampling points/edges of the clock signals ~,, ~2, and ~3. For 15 example, if Fm"~ is 1 GHz, the bandwidths of filters FL, FP and FH are 0-250 MHz, 250-500 MHz and 500 MHz-1 GHz, respectively, and the output sample rate Fs is equal to at least 2 Gigasamples/second, suitable frequencies for clock signals øl, ~Z, and ~3 are 500 MHz, 500 MHz and 1 GHz, respectively.
Again, the filters FL, FP and FH, together with the sample-and-hold circuits SHL, SHP and SHH, constitute an analysis filter bank. Also, each combination of a sample-and-hold circuit and a quantizer constitutes an analog-to-digital converter unit.
The filters XL, Xp and XH could comprise an octave filter bank as shown in Figure 9. 1'he octave filter bank comprises a first stage formed by a lowpass filter FLP
and a high pass filter FH having their inputs connected in common to receive the input signal u(t). The narrowband signal from filter FH is the high pass signal XH.
The filtered signal from filter F~ is filtered by additional two filters FL and FP
to provide the low pass signal XL and the bandpass signal XP. Filters FLP and FH would have the same bandwidth, e.g. 500 MHz, and filters FL and FP would have the same, lower bandwidth, e.g. 250 MHz.
The frequency of clock signal ~3 is one half of the rate of master clock signal CLK, and the clock signals ~2 and ~, have the same frequency equal to one half the rate of clock signal ~3.
The operation of the mufti-resolution A/D converter, which is analogous to that of the uniform analog-to-digital converter of Figure 2, will now be described with reference also to Figure 8. At the beginning of clock period T1 of main clock signal CLK, the rising edge of clock signal ~, causes sample-and-hold circuit SHL to sample narrowband signal XL. The sample is quantized by quantizer QL to produce quantized sample DL, which is clocked into register RL, as value GLI, by the rising edge at the beginning of main clock period T2. The sample-and-hold circuit SHL holds the sample for one complete cycle of clock signal ~1, and the digitized value Gel remains in the register RL for a similar length of time, specifically until the end of period TS of main clock signal CLK.
At the beginning of period T2 of clock signal CLK, the rising edge of clock signal ~3 causes sample-and-hold circuit SHH to sample high pass signal XH and the sample is quantized by quantizer QH to produce digitized value DH,. The corresponding digitized value GH, is clocked into register RH at the beginning of main clock period T3 of main clock signal CLK. In this case, digitized value GH, is stored in register RH for only two periods of main clock signal CLK.
At the beginning of period T3 of main clock signal CLK, the rising edge of clock signal ~2 causes sample-and-hold circuit SHP to sample bandpass signal XP.
1'he resulting sample is quantized by quantizer Qp and clocked into register RP by the rising edge at the beginning of period T4 of main clock signal CLK. The corresponding digitized value GPl is stored in register RP for four periods of main clock signal CLK.
The summing device 12 (Figure 9) sums the outputs of registers RL, RP and RH
at the beginning of each period of main clock signal CLK. Allowing for processing time, the result, GLl and G~ and GHO is available by the next falling edge of clock signal CLK, and is clocked into output register R~,~. Values G~ and GHO are, of course, values previously obtained by a similar process.
The sequence is repeated for subsequent samples of the narrowband signals XL, XP and XH to produce a series of values, GL, + G~ + GHO, GL, + G~ + GH,, GLl +
GPl + GHI, and so on as the digital output signal x(n) at the sampling Fe.
As before, in view of the continuous nature of the analog signal u(t) and the analysis filter bank characteristics of the A-D converter, x(n) is an accurate representation of input signal u(t), even though each of the individual sample-and-hold circuits SHL, SHP and SHH does not necessarily sample at double the maximum frequency of the corresponding one of the narrowband signals XL, XP and XH.
Various modifications may be made to the above-described embodiments without departing from the scope of the present invention. Thus, in Figures 3, 6 and 8, sampling is carried out on the rising edges of the clock signals, but it would also be possible to carry out sampling on the falling or trailing edges, in which case suitable alternative components would be selected.
It should be noted that embodiments of the invention differ from time-interleaved D-A converters in that the inputs to the A/D converter units are subband signals of the wide-band continuous time input signal u(t). Another important difference in embodiments of this invention is that, unlike the time interleaved converters, the outputs are not time-multiplexed, but rather are summed.
Referring now to Figure 10, a digital-to-analog converter suitable for converting a high speed digital signal x(n) to an analog signal u(t) comprises a bank of lower speed D-A converter units DA.o, DA, ... DAM_, having their inputs connected in common to receive the input digital signal x(n). The outputs of the D-A converters DAo-DAM_1 are applied to the inputs of a bank of narrowband filters Po, P, - PM-~, respectively, the outputs of which are summed by analog summing device 20 to form the analog output signal u(t). The bank of narrowband filters Po - PM-, and summing device 20 constitute an analog synthesis filter bank.
The bank of D-A converters DAa - DAM_1 are clocked by a corresponding plurality of clock signals ~o - ~M-, which all have the same frequency but are offset in phase relative to each other, conveniently uniformly. As in the case of the A-D
converter described hereinbefore, the phase offsets are such that each sampling point of the input signal x(n) coincides with a sampling point of one of the clock signals ~1 - ~M-1.
Although embodiments of the invention have been described and illustrated in detail, it is to be clearly understood that the same are by way of illustration and example only and not to be taken by way of the limitation, the spirit and scope of the present invention being limited only by the appended claims.
Claims (6)
1. An analog-to-digital converter for converting an analog input signal (u(t)) having a frequency up to a predetermined maximum frequency (F max) to a digital output signal (x(n)) having a predetermined output sampling rate (F S) equal to at least double the maximum frequency (F max), the analog-to-digital converter comprising:
(i) a plurality of analog narrowband filters (F0-FM-1; F L,F H,F P) for filtering the analog input signal (u(t)) to produce a corresponding plurality of narrowband signals (X0-XM-1; X L,X H,X P), each narrowband filter having a passband, the sum of the gains of the narrowband filters at any frequency within an operating frequency band of the plurality of narrowband filters being substantially unity;
(ii) a corresponding plurality of sample-and-hold devices (SH0-SHM-1;
SH L,SH H,SH P) clocked by a plurality of clock signals (.PHI.0 - .PHI.M-1), respectively, each of the plurality of clock signals having a frequency at least double the bandwidth of the corresponding narrowband filter; and (iii) a plurality of quantizers (Q0-QM-1; Q L,Q H,Q P) each connected to a respective one of the sample-and-hold devices (SH0-SHM-1; SH L,SH H,SH P) and operable to provide a digitized value of each sample held by the corresponding sample-and-hold device;
(iv) sampling and summing means (12,R0-RM-1; 12 1,12 2, 14; 12,14 1, 14 2;
R L,R H,R P) for sampling and summing the outputs of the quantizers to produce said digital output signal (x(n)), the sampling being carried out sequentially at the predetermined sampling rate (Fs) in response to an output clock signal (CLK), the frequencies and phase-relationships of the plurality of clock signals (.PHI.0 - .PHI.M-1) being such that each sample point of the output clock signal coincides with a sample point of one of the plurality of clock signals.
(i) a plurality of analog narrowband filters (F0-FM-1; F L,F H,F P) for filtering the analog input signal (u(t)) to produce a corresponding plurality of narrowband signals (X0-XM-1; X L,X H,X P), each narrowband filter having a passband, the sum of the gains of the narrowband filters at any frequency within an operating frequency band of the plurality of narrowband filters being substantially unity;
(ii) a corresponding plurality of sample-and-hold devices (SH0-SHM-1;
SH L,SH H,SH P) clocked by a plurality of clock signals (.PHI.0 - .PHI.M-1), respectively, each of the plurality of clock signals having a frequency at least double the bandwidth of the corresponding narrowband filter; and (iii) a plurality of quantizers (Q0-QM-1; Q L,Q H,Q P) each connected to a respective one of the sample-and-hold devices (SH0-SHM-1; SH L,SH H,SH P) and operable to provide a digitized value of each sample held by the corresponding sample-and-hold device;
(iv) sampling and summing means (12,R0-RM-1; 12 1,12 2, 14; 12,14 1, 14 2;
R L,R H,R P) for sampling and summing the outputs of the quantizers to produce said digital output signal (x(n)), the sampling being carried out sequentially at the predetermined sampling rate (Fs) in response to an output clock signal (CLK), the frequencies and phase-relationships of the plurality of clock signals (.PHI.0 - .PHI.M-1) being such that each sample point of the output clock signal coincides with a sample point of one of the plurality of clock signals.
2. An analog-to-digital converter according to claim 1, wherein the sampling-and-summing means (12, 12 1, 12 2 14, 14 1, 14 2, R0-RM-1) comprises means (R L - R H) for sampling the outputs of the quantizers at the predetermined rate (F S) and means (12') for summing the samples from the sampling means (R0 - RM-1).
3. An analog-to-digital converter according to claim 1, wherein the sampling-and-summing means (12, 12 1, 12 2 14, 14 1, 14 2, R0-RM-1) comprises summing means (12 1-for summing digitized values from the plurality of quantizers and sampling means (14) for sampling the summed digitized values.
4. An analog-to-digital converter according to claim 1, wherein the plurality of narrowband filters all have the same bandwidth equal to one half of said predetermined output sampling rate (Fs) divided by the number (M) of said narrowband signals (X0 - XM-1), and said plurality of clock signals (.PHI.0 -.PHI.M-1) all have the same frequency and are uniformly phase-displaced relative to each other by a phase angle equal to one cycle of said same frequency divided by the number (M) of said plurality of clock signals.
5. An analog-to-digital converter according to claim 1, wherein the plurality of analog narrowband filters have non-uniform bandwidths for filtering the analog input signal (u(t)) to produce a corresponding plurality of narrowband signals (X0 -XM-1) having different bandwidths.
6. A digital-to-analog converter, for converting a digital input signal (x(n)) into an analog output signal (u(t)), comprising an analog synthesis filter bank (DA0-DA M-1) having a plurality of inputs and a plurality of outputs, the plurality of outputs being connected in common to a summing device (2) for summing respective output signals from the synthesis filter bank to provide an analog output signal (u(t)), and a plurality of digital-to-analog converter units (DA0-DA M-1) having their inputs connected in common to receive the digital input signal (x(n)) and each having its output connected to a respective one of said plurality of inputs of the synthesis filter bank (DA0-DA M-1), the digital-to-analog converter units (DA0-DA M-1) being clocked by a plurality of clock signals (~o - ~M-1), respectively, the frequencies and relative phase differences of the plurality of clock signals ((~o - ~M-1) being arranged so that a sampling point of the input digital signal (x(n)) coincides with a sampling point of one of the plurality of clock signals (~o - ~M-1).
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA 2292718 CA2292718A1 (en) | 1998-12-21 | 1999-12-20 | High speed analog-to-digital converter and digital-to-analog converter |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA002256779A CA2256779A1 (en) | 1998-12-21 | 1998-12-21 | High speed analog-to-digital converter and digital-to-analog converter |
| CA2,256,779 | 1998-12-21 | ||
| CA 2292718 CA2292718A1 (en) | 1998-12-21 | 1999-12-20 | High speed analog-to-digital converter and digital-to-analog converter |
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| CA2292718A1 true CA2292718A1 (en) | 2000-06-21 |
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| CA 2292718 Abandoned CA2292718A1 (en) | 1998-12-21 | 1999-12-20 | High speed analog-to-digital converter and digital-to-analog converter |
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1999
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